I want to show this but I have problem with where I should start .
For two interpretation function $I$,$J$ , we define $I \le J$ when for every atom $p$ we have $I(p) \le J(p)$.We define proposition A is increasing if for two interpretation function $I,J$ that $I \le J$ we have $I(A)\le J(A)$.
Now I want to prove this:
Proposition A is increasing if only and if for every atom $p$ and two proposition $B$ and $C$ that $B \models C$ we have $A[p/B] \models A[p/C]$